First Online: 18 November 2016Received: 26 September 2016Accepted: 13 November 2016Abstract

The large-N limit of ABJM theory is holographically dual to M-theory on AdS4 × S-ℤk. The 3-sphere partition function has been obtained via localization, and its leading behavior FABJM ∼ kN is exactly reproduced in the dual theory by tree-level supergravity. We extend this comparison to the sub-leading \ \mathcal{O}\left{N}^0 ight \ order by computing the one-loop supergravity free energy as a function of k and comparing it with the ABJM result. Curiously, we find that the expressions do not match, with FSUGRA ∼ k, while FABJM ∼ k. This suggests that the low-energy approximation ZM-theory = ZSUGRA breaks down at one-loop order.